the d20 is the basic main dice you do for skill checks and battle. for skill checks you roll d20 and add up the amount you get plus whatever bonus you get from a skill bonus.
EX: I rolled a 9 for perception check and I am trained in it and rave a rank in it so the bonus is +5 plus my wisdom bonus which is +3 so all together I get 17 total.
for battle you roll it and the goal is to roll a number higher then the AC (armor class) and add together your base attack bonus or as its called B.A.B
EX: the enemy has a AC of 12 and I rolled a 7, but with my B.A.B is a +6 so all together its 13 so I land the hit.
note that if your using a weapon with both hand (like swinging an axe and the character is holding it with both hands) then you add the strength bonus to the damage result.

all other dice is used for weapons damage roll, or a spells damage roll.